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Have you ever given your students an experience with manipulatives and then found when you shifted over to a textbook that the students didn’t make the connection between the two experiences? As a curriculum developer and researcher, I am constantly looking for more ways for students to make connections from the concrete (manipulatives) to the representational (pictures) to the abstract (numbers).I think word problems can help us do this because they are from the real world, and students can visualize themselves in the given situation.Now, word problems can be challenging for students because they require the students to have an understanding of the context or setting, an ability to read, and an understanding of the math concepts involved. Today I want to share with you something I recently field tested that allows kids to work with word problems and focuses on developing a better understanding of division. The students were doing division, but I have also created the sentence frames for you to do it with multiplication.

1. Start by having students work with manipulatives (concrete) and solve division or multiplication problems. If you want to use the setting of astronauts you can cut them out from the black line master. Solve problems like the following:2. You can use the table to choose different problems and a class.3. After students are comfortable with solving problems using the manipulatives, you can give them the task to independently represent the problem with the pictures of the astronauts on a word problem page.Students can do multiple problems,choosing easy or difficult problems to solve from the table. You can also later put the solved problems into a class book about division.When students are doing word problems they are interacting with a variety of the Mathematical Practice Standards:MP.1 Make sense of problems and persevere in solving them.MP.2 Reason abstractly and quantitatively.MP.6 Attend to precision.MP.7 Look for and make use of structure.Building the concept of division through solving word problems is so beneficial because the word problems connect the real world with math, engage the students, and support mathematical communication.How have you helped students connect the real world and the mathematical world?

Why do you teach? I remember when I first came into the profession it was because I enjoyed students and wanted to make a difference. I still love watching movies of teachers that have gone into challenging situations and inspired students to think differently. These teachers empowered the students to be all that they were… Continue Reading

In my last post, Tangrams: A World of Geometry, Part Two, I talked about the thirteen convex polygon shapes that can be formed with the seven tangram pieces. In the video, I showed how to make five of them, and then I left a challenge for you to look for the remaining eight convex shapes.… Continue Reading

In work or social settings it is common to hear the question, “Have you read a good book lately?” The question often starts a lively sharing session about books that elicit pleasure, profundity, or insight. A population that regularly engages in these discussions is an indicator of a literate society. As those appointed by society… Continue Reading

Word problems are typically not students’ or teachers’ favorite part of the math lesson. When I talk with teachers, they are frustrated with teaching multiplication word problems. I think one of the things we have been missing is teaching students the structure of what is involved in any multiplication word problem. “Look for and make… Continue Reading

How early should we teach words like half, thirds, and fourths to children? I know that I have often heard that we give young children things they are not developmentally ready for, and I agree. But when it comes to having language identify a concrete experience, I think children can handle it. I was measuring… Continue Reading

How to Equip Your Students to Better Understand Multiplication, Part One As I have coached and taught in the classroom, the three most popular ways to describe multiplication is showing ______ groups of ______, using repeated addition and making arrays. Now all of these methods have their place in a student’s understanding of multiplication, but… Continue Reading

I was reading Inchworm and a Half with my 6-year-old daughter, Bethany, last night for the 40th time. She loves reading the section, “Squirmy, wormy, hoppity-hoop! We measure everything, loopity loop.” Even before she could read books she memorized this section and would “read” it. The book is about an inchworm that loves to measure… Continue Reading

What would you or your students say math is? Some common answers could be numbers, addition, subtraction . . . Below are the posters a group of AIMS trainers created answering that question. Most people don’t understand what math really is. If you have read some of my previous posts, you know my elementary and… Continue Reading

I never liked word problems as a student. It was difficult for me to figure out which procedure to use, but I really didn’t like problems like this: Robert is three times as old as his younger brother Mark. Mark is 7 years old. How old is Robert? As I reflect on my experience, I… Continue Reading